Heat transfer apparatus

ABSTRACT

A heat transfer apparatus and related methods are provided. The heat transfer apparatus and related methods more evenly distribute fluid flow in two-phase heat exchange systems by restricting fluid flow to one or more tube.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application claims priority to U.S. Provisional Patent ApplicationSer. No. 60/898,337, filed Jan. 30, 2007, and U.S. patent applicationSer. No. 12/022,673, filed Jan. 30, 2008, now U.S. Pat. No. 8,424,551,the entire disclosures of which are incorporated herein by reference.

FIELD

The present invention relates generally to heat exchange systems. Morespecifically, the present invention is concerned with (1) methods tooptimize flow in two-phase heat exchange systems and (2) devices andmethods that incorporate restricted flow tubes to optimize even fluidflow in two-phase systems.

BACKGROUND References

The following references are cited by number throughout this disclosureand provide general background information. Applicant makes nostatement, inferred or direct, regarding the status of these referencesas prior art. Applicant reserves the right to challenge the veracity ofstatements made in these references, which are incorporated herein byreference.

1. Chisholm, D. (1983) Two-Phase Flow in Pipes and Heat Exchangers.George Godwin/Institution of Chemical Engineers, London. 1-24,106-113,123-128.

2. Paliwoda, A. (1992) “Generalized Method of Pressure Drop CalculationAcross Pipe Components Containing Two-Phase Flow of Refrigerants”.International Journal of Refrigeration. Vol 15, No. 2, p. 119-125.

3. Watanabe, M., Katsuta, M. and Nagata, K. (1995) Two-phase flowdistribution in multi-pass tube modeling serpentine type evaporator,Proceedings of the ASME/JSME Thermal Engineering Conference, 2, p.35-42.

4. Campagna, Michael 2001, An Evaporator Model which accounts for theMal-distribution of Refrigerant applied to evaluate the Performance ofInlet Manifold Flow Distributors, Masters Thesis, Bradley University.

Two-phase flow, which is flow of fluids in a liquid phase and a vapor orgas phase, is encountered extensively in the air-conditioning, heating,and refrigeration industries. In order to avoid uneven refrigerantdistribution in evaporator manifolds, the behavior of tubes andmanifolds with two-phase flow needs to be understood. With evendistribution of refrigerant in tubes, the size of the evaporator can bereduced while maintaining cooling capacity and compressor powerconsumption. This reduces the initial cost of the system withoutchanging its performance. Uneven distribution of liquid is the mainfactor preventing micro-channel heat exchangers from replacing plate-finand fin and tube heat exchangers in most applications. Micro-channelheat exchangers typically have 20% more heat exchanger area for the samepackage volume compared to plate-fin heat exchangers.

Campagna (reference 4) worked on simulating the uniform, evenlydistributed flow of liquid in the manifold using parallel perforatedplates, inserted into the manifold, supported by two threaded rods. Onedisadvantage to inserting flow distribution plates into the manifold isthat it does not allow for easy access and adjustment over the course oftime and usage. What is needed is a device and/or method to alter theflow of fluid in a heat exchanger to be more evenly distributed, thatcan be easily and quickly adjusted without disassembling the heattransfer apparatus.

SUMMARY

An object of the instant invention is to provide a heat transferapparatus and method. Another object of the instant invention is toprovide a more efficient heat transfer device and method that moreevenly distributes the flow of fluid. Still another object of theinstant invention is to provide a method of modeling the optimization ofheat transfer efficiency.

Objects of the instant invention are accomplished through the use of aheat transfer apparatus comprising a manifold and a plurality of tubesextending from the manifold. In a preferred embodiment, the manifoldcomprises an inlet and a plurality of mini heat exchanger channelsconnected to the inlet, wherein each mini heat exchanger channel isoperably connected to a tube. In a preferred embodiment at least onetube comprises a fluid flow restrictor. In other preferred embodiments,each of the tubes includes a fluid flow restrictor. The fluid flowrestrictors of the instant invention are not limited to a particularmeans or structure, but non-limiting examples in some configurationsinclude: a tube restrictor valve; a tube crimp or a restriction tubesegment (such as a reducer coupler, wherein the restriction tube segmenthas an inside diameter smaller than the inside diameter of a tube withno fluid flow restrictor). The instant invention allows the flow offluid to be more evenly distributed among the plurality of tubes than aheat transfer apparatus with no fluid flow restrictor. If each of thetubes of the instant invention are restricted to its respectivepreferred predetermined amount, the flow of fluid is generally evenlydistributed among the tubes, resulting in a more efficient transfer ofheat. In preferred embodiments, the flow of fluid is about equallydistributed among the tubes. In preferred embodiments, the fluid isliquid, vapor or some combination of both liquid and vapor. In someembodiments, the fluid is a refrigerant.

Objects of the instant invention are also accomplished through a methodof improving the efficiency of heat transfer comprising restricting theflow of fluid in at least one tube of a heat transfer apparatus to apredetermined amount. In some embodiments of the instant invention thepredetermined amount of flow is a function of the position of the tubealong the manifold relative to a fluid inlet position of the manifold.In some embodiments, the flow of fluid is restricted in each of thetubes of the heat transfer apparatus. The restriction of fluid flow isnot limited to a particular method, means or structure, but non-limitingexamples in some configurations include, restricting fluid flow using atube restrictor valve, a tube crimp or a restriction tube segment (suchas a reducer coupler, wherein the restriction tube segment has an insidediameter smaller than the inside diameter of a tube with no fluid flowrestrictor). If only one of the tubes of the instant invention isrestricted, it allows the flow of fluid to be more evenly distributedamong the plurality of tubes than a heat transfer apparatus with nofluid flow restrictor. If each of the tubes of the instant invention arerestricted to its respective preferred predetermined amount, the flow offluid is generally evenly distributed among the tubes, resulting in amore efficient transfer of heat. In preferred embodiments, the flow offluid is about equally distributed among the tubes. In preferredembodiments the fluid is liquid, vapor or some combination of bothliquid and vapor. In some embodiments, the fluid is a refrigerant.

Objects of the instant invention are also accomplished through a methodof modeling the optimization of heat transfer efficiency of a two-phaseheat transfer apparatus, the apparatus comprising a manifold and aplurality of tubes extending from the manifold. The method includes thesteps of estimating sudden expansion two-phase pressure drop at an inletof the manifold; predicting the two-phase pressure drop across tubes ofthe manifold; determining parameters for each tube of the apparatusrelated to an uneven fluid flow distribution; determining parameters foreach tube related to an even flow distribution; and determining apreferable restriction cross-sectional area of each tube. In someembodiments, the apparatus further comprises a fluid flow restrictorconnected to at least one of the plurality of tubes, and the methodfurther comprises the steps of calibrating a dimensionless position ofeach fluid flow restrictor to a restriction cross-sectional area of eachrespective tube; and determining zero offset values. In someembodiments, the method further comprises restricting thecross-sectional area of at least one tube to the preferable restrictioncross-sectional area. In other embodiments, the method further comprisesrestricting the cross-sectional area of each tube to each tube'srespective preferable restriction cross-sectional area. The restrictionof fluid flow is not limited to a particular method, means or structure,but non-limiting examples in some configurations include, restrictingfluid flow using a tube restrictor valve, a tube crimp or a restrictiontube segment (such as a reducer coupler, wherein the restriction tubesegment has an inside diameter smaller than the inside diameter of atube with no fluid flow restrictor). If only one of the tubes of theinstant invention is restricted, it allows the flow of fluid to be moreevenly distributed among the plurality of tubes than a heat transferapparatus with no fluid flow restrictor. If each of the tubes of theinstant invention are restricted to its respective preferredpredetermined amount, the flow of fluid is generally evenly distributedamong the tubes, resulting in a more efficient transfer of heat. Inpreferred embodiments, the flow of fluid is about equally distributedamong the tubes. In preferred embodiments the fluid is liquid, vapor orsome combination of both liquid and vapor. In some embodiments, thefluid is a refrigerant.

The foregoing and other objects are intended to be illustrative of theinvention and are not meant in a limiting sense. The skilled artisan canreadily deploy in the practice of this invention alternative methods forcontrolling the flow of liquid in one or more tubes to affect the moreeven distribution of liquid across the tubes of the manifold to attainmore efficient heat transfer of a two-phase heat transfer apparatus.Many possible embodiments of the invention may be made and will bereadily evident upon a study of the following specification andaccompanying drawings comprising a part thereof. Various features andsubcombinations of invention may be employed without reference to otherfeatures and subcombinations. Other objects and advantages of thisinvention will become apparent from the following description taken inconnection with the accompanying drawings, wherein is set forth by wayof illustration and example, an embodiment of this invention and variousfeatures thereof.

BRIEF DESCRIPTION OF THE DRAWINGS

A preferred embodiment of the invention, illustrative of the best modein which the applicant has contemplated applying the principles, is setforth in the following description and is shown in the drawings and isparticularly and distinctly pointed out and set forth in the appendedclaims.

FIG. 1 shows a heat transfer apparatus of a first embodiment of theinstant invention.

FIG. 2 shows a cross-section of the heat transfer apparatus of FIG. 1along the line 2-2 shown in FIG. 1.

FIG. 3 shows a cross-section of the heat transfer apparatus of FIG. 1along the line B-B shown in FIG. 2.

FIG. 4 shows an uneven distribution pattern of a heat transfer apparatusof the prior art.

FIG. 5 shows empirically measured standard deviation of flow through aheat transfer apparatus of the prior art as a function of cooling load.

FIG. 6 shows empirically measured standard deviation of flow through aheat transfer apparatus of the prior art as a function of refrigerantquality.

FIG. 7 shows empirically measured standard deviation of flow through aheat transfer apparatus of the prior art as a function of water massflow rate.

FIG. 8 shows empirically measured standard deviation of flow through aheat transfer apparatus of an embodiment of the instant invention as afunction of cooling load.

FIG. 9 shows empirically measured standard deviation of flow through aheat transfer apparatus of an embodiment of the instant invention as afunction of refrigerant quality.

FIG. 10 shows empirically measured standard deviation of flow through aheat transfer apparatus of an embodiment of the instant invention as afunction of water mass flow rate.

FIG. 11 shows empirically measured pressure drop in the manifold of aheat transfer apparatus of an embodiment of the instant inventioncompared with that of the prior art as a function of water mass flowrate.

FIGS. 12, 12-A, 12-B, 12-C and 12-D show a flowchart for a method ofpredicting the cross sectional restriction area of tubes of a heatexchanger of a preferred embodiment of the instant invention.

FIG. 13 shows empirically measured water and air loss coefficients as afunction of dimensionless valve settings that have been correlated topredetermined cross-sectional restriction areas.

DETAILED DESCRIPTION

As required, several detailed embodiments of the present inventiveconcept are disclosed herein; however, it is to be understood that thedisclosed embodiments are merely exemplary of the principles of theinventive concept, which may be embodied in various forms. Therefore,specific structural and functional details disclosed herein are not tobe interpreted as limiting, but merely as a basis for the claims and asa representative basis for teaching one skilled in the art to variouslyemploy the present inventive concept in virtually any appropriatelydetailed structure.

Referring to FIG. 1, a heat transfer apparatus (10) of one embodiment ofthe instant invention is shown. The apparatus (10) of FIG. 1 includes amanifold (20) with a fluid inlet (26) operably connected to heatexchanger channels (22) and six tubes (30) extending from the manifold(20). Some of the tubes (30) include a tube restrictor valve (40). Fluidflows from the inlet (26), through a manifold chamber (24), through theheat exchanger channels (22), and out through the tubes (30).

Restricting the tubes improves the uniformity of the mass distributionbetween heat exchanger tubes. This was demonstrated experimentally as isdiscussed in further detail below with respect to FIGS. 1-11 and 13. Twoheat transfer devices were built and tested. A first heat transferapparatus (10), shown in FIGS. 1-3, included six tubes (30) extendingfrom the manifold (20). The second heat transfer apparatus included 20tubes extending from the manifold. Flow distribution was measuredaccording to standard deviation of liquid mass flow through the tubes.Flow distribution was compared for the heat transfer devices with nofluid flow restrictors versus the same two heat transfer devices with apinch valve on each of the tubes, with the pinch valve set to apredetermined preferred restriction cross-sectional area. Thepredetermined preferred restriction cross-sectional area was determinedusing an embodiment of a method of modeling the optimization of heattransfer efficiency of a two-phase heat transfer apparatus of theinstant invention, as is further discussed below with respect to theflow chart of FIG. 12. The efficiency of the heat transfer devices wasimproved as the fluid flow was more evenly distributed by using thepinch valves. The amount of improvement varied from case to case, but inthis example, the average standard deviation of unrestricted flow wasreduced dramatically from 9.09 [kg/hr] to 0.26 [kg/hr] when the tubeswere restricted. Second, at equal mass flow rates in situations wherethe flow is more evenly distributed, the pressure drop through themanifold was reduced.

There are many forces (inertial, gravitational, friction, etc.) withinconventional heat exchanger geometries which direct more liquid to entersome heat exchanger tubes over others. To counter act these forces anadditional restriction is applied to the tubes where there is excessliquid flow. Rather than placing an insert in the manifold, as taught byCampagna (reference 4) each tube of an evaporator was equipped with atube restrictor valve (40), also called a pinch valve, as shown in FIGS.1 to 3. When the valves (40) were properly adjusted, liquid mass flowwas about evenly distributed among the tubes. FIG. 4 shows the unevendistribution flow pattern of a heat transfer apparatus with 20 tubes,wherein none of the tubes include a fluid flow restrictor.

The measure of non-uniformity of the flow distribution was quantifiedusing the statistical measure of standard deviation. A standarddeviation value of zero indicates that the distribution of flow wasuniform. The larger the standard deviation the greater is themal-distribution of liquid among the tubes. In the unrestricted case,depicted in FIG. 4, the distribution is uneven. In horizontal manifoldswith upward flow in the tubes, the tubes farthest from the inletreceived high liquid flow rate. The non-uniformity of flow distributionwhen the tubes are not restricted is very high. The average standarddeviation for all experiments was 9.09 [kg/hr]. FIGS. 5, 6 and 7 depictempirically measured standard deviation of flow distribution through aheat transfer apparatus, without any fluid flow restrictor, as afunction of cooling load, quality and liquid mass flow rate,respectively.

For the same flow rates of air and water, the experiments were conductedrestricting the tubes by using flow restriction valves. For each tube, apreferable restriction cross-sectional area was determined using anembodiment of a method of modeling the optimization of heat transferefficiency of a two-phase heat transfer apparatus of the instantinvention, as is further discussed below with respect to the flow chartof FIG. 12. The tubes were restricted to the predetermined amounts. Thestandard deviation of the liquid mass fraction was drastically reduced,indicating more uniform flow distribution. The distribution of flowafter restricting the tubes with valves was greatly improved. Theaverage standard deviation for all experiments in even flow case isdrastically reduced to 0.26 [kg/hr]. The non uniformity of liquid massflow rates in 90% of the tubes were within +/−10%. FIGS. 8, 9 and 10depict empirically measured standard deviation of flow distributionthrough a heat transfer apparatus, with pinch valves set to thepredetermined preferred restriction cross-sectional area on each tube,as a function of cooling load, quality and liquid mass flow rate,respectively.

FIG. 11 depicts empirically measured pressure drop in the manifold of aheat transfer apparatus with and without a fluid flow restrictor as afunction of water mass flow rate. FIG. 11 shows that the pressure dropin the manifold decreases for restricted flow compared to theunrestricted flow.

In this example, it was necessary to develop a computer design tool todetermine a preferable restriction cross-sectional area for a tube. FIG.12 depicts a flowchart for predicting the cross sectional restrictionarea of tubes. FIGS. 12-A, 12-B, 12-C and 12-D are continuations of theflowchart of FIG. 12. The design tool was validated using pinch valveson tubes where air and water simulated two-phase refrigerant flow. Theuncertainty in measuring the area ratio using the instruments was within4% full scale. The error in predicting the cross-sectional area ratiousing the design tool was less than 6%.

Setting the flow restriction valve was based on the loss coefficient ofthe valve and the liquid flow rate through each tube in themal-distributed case. The loss coefficient was determined for aparticular valve using single phase pressure drop correlations. Theconservation of momentum was applied to a component (e.g. valve)resulting in Equation 1.

$\begin{matrix}{{\Delta\; P_{1F}} = {\xi\frac{\rho{\overset{\cdot}{*V}}^{2}}{2\; g_{c}}}} & \lbrack 1\rbrack\end{matrix}$

Where,

ΔP_(1F), is the single-phase pressure drop (lb_(f)/ft²)

ξ the single-phase loss coefficient (−)

ρ is the density of the single phase fluid (lb_(m)/ft²)

V is the velocity of flow (ft/s)

g_(c) is the constant of proportionality for Newton's 2^(nd) Law (32.2lb_(m)−ft/lb_(f)−s²)

In this example, the loss coefficient was empirically demonstrated to bethe same whether the flow was liquid or gas. The two-phase pressure dropwas determined using single phase loss coefficient and Paliwoda's(reference 2) two-phase multiplier (β_(c)) and two phase pressure dropfactor (θ) using the correlation.

$\begin{matrix}{{\Delta\; P_{2F}} = {\xi\frac{\overset{{^\circ}}{{\overset{.}{m}}^{2}}}{2\;\rho^{''}g_{c}}\beta_{c}}} & \lbrack 2\rbrack \\{\beta_{c} = {{\left\lbrack {\vartheta + {{C\left( {1 - \vartheta} \right)}x}} \right\rbrack\left( {1 - x} \right)^{0.333}} + x^{2.276}}} & \lbrack 3\rbrack \\{\vartheta = {\frac{\Delta\; p^{\prime}}{\Delta\; p^{''}} = {\frac{\rho^{''}}{\rho^{\prime}}\left( \frac{\eta^{\prime}}{\eta^{''}} \right)^{0.25}}}} & \lbrack 4\rbrack\end{matrix}$

Where,

{dot over (m)} is the mass flux (lb_(m)/ft²)

η′ is the single-phase dynamic viscosity

η″ is the two-phase dynamic viscosity

x is vapor mass fraction (−)

C is an empirical coefficient

The input variables are mass flow rates of water ({dot over (m)}_(w)),and air ({dot over (m)}_(a)), pressure at the inlet to the manifoldP_(in), pressure drop across the manifold ΔP_(manifold), temperatures ofair and water at the entrance of manifold, number of tubes, liquid flowrates through the tubes without restriction

${\sum\limits_{i = 1}^{tubes}{\overset{.}{m}}_{{i\_ mal}\mspace{14mu}{dist\_ water}}},$diameter of tubes and diameter at the inlet of the manifold andtwo-phase loss coefficient for the sudden expansion at the inlet.

The first step in the model is to estimate sudden expansion two-phasepressure drop at the inlet of the manifold. The single-phase pressuredrop at the inlet can be determined based on average hydraulic diameterat the inlet of the manifold and the mass flux density of the two-phasemixture. The single-phase loss coefficient ξ_(exp), can be obtained froma table of values given by Paliwoda (reference 2) based on the square ofthe ratio of diameters, (d/D)² where, d, is the inlet pipe diameter andD, is the manifold hydraulic diameter. The two-phase pressure drop isestimated by multiplying the single-phase pressure drop with a two-phasemultiplier β_(exp), Equation [3]. The pressure at the inlet to the1^(st) heat exchanger tube is the difference of the pressure at theinlet and the two-phase pressure drop at the expansion.

The second step is to predict the two-phase pressure drop in themanifold. This can be determined by two-phase pressure drop correlationwith a manifold loss coefficient using equation [2]. The single-phaseloss coefficient across the manifold was determined experimentally bymeasuring the pressure drop across the manifold using water at a flowrate of 77 kg/hr, which translates to an average velocity of 26.75 in/sand Reynolds number 5,000. The manometer used for the measurement of thepressure drop in the manifold has an uncertainty 0.001 in H₂O.

The third step is to determine the parameters for each tube of the heatexchanger related to uneven flow distribution. Pressure at the inlet toeach of the mini-heat exchanger tubes can be determined using Equations6 and 7. Then, this pressure drop was used with Equation 5 to determinethe two-phase loss coefficient, C_(sec), which is a sub term in the twophase multiplier (see Equation 3).

$\begin{matrix}{{\overset{last}{\sum\limits_{i = 1}}P_{{in\_ HX}{\lbrack i\rbrack}}} = {\xi_{manifold} \cdot \beta_{i} \cdot \frac{\overset{{^\circ}}{m_{{uneven}{\lbrack i\rbrack}}}}{2 \cdot g_{c} \cdot \rho_{{air}{\lbrack i\rbrack}}}}} & \lbrack 5\rbrack \\{{\overset{{last} - 1}{\sum\limits_{i = 1}}P_{{in\_ HX}{\lbrack{i + 1}\rbrack}}} = {P_{{in\_ HX}{\lbrack i\rbrack}} - \frac{P_{{in\_ HX}\lbrack 1\rbrack} - P_{{in\_ HX}{\lbrack{last}\rbrack}}}{tubes}}} & \lbrack 6\rbrack \\{P_{{in\_ HX}{\lbrack 1\rbrack}} = {P_{in} - {\Delta\; P_{\exp}}}} & \lbrack 7\rbrack\end{matrix}$

The mass flux density is based on the mass of both the fluids of the twophase flow at each tube. The area considered to calculate the mass fluxdensity is the cross-sectional area of the heat exchanger tube. Todetermine C_(sec), the air mass flow rates at each tube for uneven flowneeded to be determined. Hence, there is one more variable than theequations required for the number of tubes. The extra variable can beaddressed using mass balance for the air flow which equates the sum ofmass of air at all tubes (calculated) to the mass of air at the inlet(measured).

The fourth step is to repeat step three and evaluate the even flowdistribution parameters. Using the two phase loss coefficient, C_(sec),this is a result from step three, ξ_(tube) the single phase losscoefficient for each tube which is a function of restriction that causeseven flow for each tube can be determined. On the other hand, usingEquation 1, ξ_(tube) can be experimentally determined using a singletube by varying restriction at the valve. Results showed that the singlephase loss coefficient is same for the fluid whether it is air or water.

An empirical correlation for valve position as a function of ξ_(tube)was measured. The data obtained which is shown as FIG. 13 were fittedwith three different polynomial equations in a piece-wise manner asshown in equations 8 to 10.Valve position=−2.6016*ξ_([i])+8.9735 for ξ<1.16  [8]Valve position=0.0019*ξ_([i]) ²−0.1442*ξ_(└i┘)+5.8411 for1.16<ξ<52.43  [9]Valve position=−0.0016*ξ_([i])+3.582 for 52.43<ξ<372.21  [10]

Correction factor [K] was introduced in calculating even mass flow rateof air through each tube to limit the ξ_(tube[j]) values within thevalid range to determine the valve position between 0 and 9.

The fifth step is to calibrate the fluid flow restrictor. In thisexample, pinch valves were used. The pinched valves used for restrictionwere labeled with graduations. These graduations do not have anydimensional significance other than 9 is fully open and 2.8 is fullyclosed for ¼ inch ID ( 5/16 inch OD) flexible tube. Experimentation wasdeveloped to correlate the graduations to the area of restriction.

Using a simple experimental setup, the pinch valve was calibrated with asecond degree polynomial correlation shown as equation 11 betweengraduation and cross-sectional area after restriction. The correlationis based on two sets of data collected separately to minimize the error.The developed correlation best fits the data with an R-Square(R²)=0.9933.Cross-Sectional Area=−0.0008*(vp)²+0.0186*(vp)−0.0488  [11]

Where,

vp is the valve position.

The sixth step is to determine the zero offset values. In order to limitthe valve settings within the fully open area in all cases, zero offsets[A=1.1024, B=1 and C=0.8975] were iteratively determined and used asmultiples for the constant term of the cross-sectional area equation 11,for the valve position equations 8 to 10 respectively.

The seventh step is to determine a preferable restrictioncross-sectional area of each tube. A cross-sectional area ratio of eachtube is specified such that the fluid in the manifold at a specifiedoperating condition is more evenly distributed. The area ratio is equalto the final area/fully open area. The final area is the area of thetube after restriction and the fully open area is the tubecross-sectional area at no restriction. In this example, the pinch valvewas used to change the area ratio. An area ratio equal to one is fullyopen and zero is fully closed. The uncertainty in predicting the arearatio by the design tool using the instruments was within 4%.

In the foregoing description, certain terms have been used for brevity,clearness and understanding; but no unnecessary limitations are to beimplied therefrom beyond the requirements of the prior art, because suchterms are used for descriptive purposes and are intended to be broadlyconstrued. Moreover, the description and illustration of the inventionsis by way of example, and the scope of the inventions is not limited tothe exact details shown or described.

Although the foregoing detailed description of the present invention hasbeen described by reference to an exemplary embodiment, and the bestmode contemplated for carrying out the present invention has been shownand described, it will be understood that certain changes, modificationor variations may be made in embodying the above invention, and in theconstruction thereof, other than those specifically set forth herein,may be achieved by those skilled in the art without departing from thespirit and scope of the invention, and that such changes, modificationor variations are to be considered as being within the overall scope ofthe present invention. Therefore, it is contemplated to cover thepresent invention and any and all changes, modifications, variations, orequivalents that fall with in the true spirit and scope of theunderlying principles disclosed and claimed herein. Consequently, thescope of the present invention is intended to be limited only by theattached claims, all matter contained in the above description and shownin the accompanying drawings shall be interpreted as illustrative andnot in a limiting sense.

Having now described the features, discoveries and principles of theinvention, the manner in which the invention is constructed and used,the characteristics of the construction, and advantageous, new anduseful results obtained; the new and useful structures, devices,elements, arrangements, parts and combinations, are set forth in theappended claims.

It is also to be understood that the following claims are intended tocover all of the generic and specific features of the invention hereindescribed, and all statements of the scope of the invention which, as amatter of language, might be said to fall therebetween.

What is claimed is:
 1. A heat transfer apparatus comprising: a manifoldand a plurality of tubes extending from the manifold so as to enablefluid to flow from the manifold through the plurality of tubes; whereinthe manifold comprises an inlet and a plurality of heat exchangerchannels connected to the inlet, each heat exchanger channel beingoperably connected to one of the plurality of tubes; and wherein atleast one tube includes a fluid flow restrictor such that fluid flowthrough the at least one restricted tube is reduced so as to more evenlydistribute fluid flow through the plurality of tubes.
 2. The apparatusof claim 1, wherein each of the plurality of tubes includes a fluid flowrestrictor.
 3. The apparatus of claim 1, wherein the fluid flowrestrictor is selected from the group consisting of a tube restrictorvalve, a tube crimp and a restriction tube segment, wherein therestriction tube segment has an inside diameter smaller than the insidediameter of a tube with no fluid flow restrictor.
 4. The apparatus ofclaim 1, wherein the fluid is liquid, vapor or some combination of bothliquid and vapor.
 5. The apparatus of claim 4, wherein the fluid is arefrigerant.
 6. A heat transfer apparatus comprising: a manifold and aplurality of tubes extending from the manifold; wherein the manifoldcomprises an inlet and a plurality of heat exchanger channels connectedto the inlet, each heat exchanger channel being operably connected toone of the plurality of tubes; wherein at least one tube includes afluid flow restrictor; wherein in each tube that includes a fluid flowrestrictor, a flow of fluid is restricted to a predetermined amount,said predetermined amount is such that additional restriction is appliedto a tube where there would otherwise be excess fluid flow, whereby aforce which directs more fluid to enter one tube over another iscountered.
 7. The apparatus of claim 6, wherein each of the plurality oftubes includes a fluid flow restrictor.
 8. The apparatus of claim 6,wherein the fluid flow restrictor is selected from the group consistingof a tube restrictor valve, a tube crimp and a restriction tube segment,wherein the restriction tube segment has an inside diameter smaller thanthe inside diameter of a tube with no fluid flow restrictor.
 9. Theapparatus of claim 6, further comprising a fluid, wherein the fluid isliquid, vapor or some combination of both liquid and vapor.
 10. Theapparatus of claim 9, wherein the fluid is a refrigerant.
 11. Theapparatus of claim 6, wherein said predetermined amount is determinedaccording to a method comprising: estimating sudden expansion two-phasepressure drop at an inlet of the manifold; predicting the two-phasepressure drop across the manifold; determining parameters for each tubeof the apparatus related to an uneven fluid flow distribution;determining parameters for each tube related to an even flowdistribution; and determining a preferable restriction cross-sectionalarea of each tube.
 12. The apparatus of claim 11, wherein said methodfurther comprises: calibrating a dimensionless position of each fluidflow restrictor to a restriction cross-sectional area of each respectivetube; and determining zero offset values.